It's because both communities have a recent history of suffering intolerance, bigotry and hyperbolic media persecution. Islam, obviously, more recently than the LGBT community.

In any case, the idea that Muslims automatically agree with Sharia law and want to implement it in western society is absolute bull**** to anyone who spends even a little time informing themselves by actually spending time with Muslims and talking to them, rather than reading tabloids and listening to right-wing podcasts; as most people, while being devout (to either religion) aren't as homophobic as a lot of people would like us to think.